scholarly journals Generalized Continuity Equation for Quasi-Hermitian Hamiltonians

10.14311/1803 ◽  
2013 ◽  
Vol 53 (3) ◽  
Author(s):  
Amine B. Hammou
Keyword(s):  
Continuity Equation ◽  
Delta Function ◽  
Reflection And Transmission Coefficients ◽  
Reflection And Transmission ◽  
One Dimensional ◽  
Transmission Coefficients ◽  
Generalized Continuity ◽  
Unitarity Relation ◽  
Function Potential

The continuity relation is generalized to quasi-Hermitian one-dimensional Hamiltonians. As an application we show that the reflection and transmission coefficients computed with the generalized current obey the conventional unitarity relation for the continuous double delta function potential.

scholarly journals Quantum Mechanical Reflection and Transmission Coefficients for a Particle through a OneDimensional Vertical Step Potential

2019 ◽  
Vol 8 (11) ◽  
pp. 2882-2886
Keyword(s):  
Laplace Transformation ◽  
Reflection And Transmission Coefficients ◽  
Quantum Mechanical ◽  
Mathematical Tool ◽  
Science And Engineering ◽  
Step Potential ◽  
Reflection And Transmission ◽  
One Dimensional ◽  
Transmission Coefficients ◽  
Vertical Step

In this paper, we illustrate an application of the Laplace transformation for finding the quantum mechanical Reflection and Transmission coefficients for a particle through a one-dimensional vertical step potential. Quantum mechanics is one of the branches of physics in which the physical problems are solved by algebraic and analytic methods. By applying the Laplace transformation, we can find the quantum mechanical Reflection and Transmission coefficients for a particle through a one-dimensional vertical step potential. Generally, the Laplace transformation has been applied in different areas of science and engineering and makes it easier to solve the problems inengineering applications. It is a mathematical tool which has been put to use for solving the differential equations without finding their general solutions. It has applications in nearly all science and engineering disciplines like analysis of electrical circuits, heat and mass transfer, fluid dynamics, nuclear physics, process controls, quantum mechanical problems,etc.

Evaluation of Moisture Content in Concrete with Microwave

2006 ◽  
Vol 312 ◽  
pp. 311-318 ◽  
Author(s):  
Xiao Ming Wang ◽  
Yinghao Teo ◽  
Wing K. Chiu ◽  
Greg Foliente
Keyword(s):  
Moisture Content ◽  
Water Content ◽  
Condition Monitoring ◽  
Reflection And Transmission Coefficients ◽  
Physical Change ◽  
Microwave Propagation ◽  
Reflection And Transmission ◽  
One Dimensional ◽  
Transmission Coefficients ◽  
Permittivity And Permeability

Generally, any chemical or physical change in a material may cause variation in its permittivity and permeability. The propagation of microwave through the material can be affected by these variation in properties. The analysis of microwave propagation through materials may therefore provide a means for condition monitoring. This paper utilizes a one-dimensional scenario, demonstrating the feasibility to link measurable reflection and transmission coefficients of microwave to concrete permittivity and permeability, which are essentially associated with water content in concrete. As a result, water content can then be monitored through the measurement of these coefficients. The study also demonstrates the feasibility of using the same technique to estimate the thickness of the concrete that microwave propagates through.

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